Aircraft: LIGHT TRANSPORT
Phase of flight: Descent
Anomaly: ATC Issue All Types; Airspace Violation All Types; Deviation / Discrepancy - Procedural Published Material / Policy

This aircraft called asking for lower; they were no longer on my scope; I did not know who was calling. The sector was completely out of control; we had a tracker; and D side. The level of traffic at the same time was unheard of; uncalled for and completely irresponsible. There was no in trail spacing for ZZZ1 and ZZZ2 arrivals; the departures out of ZZZ2; ZZZ3; And ZZZ1 were not stopped. The sector was not split. I do not belief we had the staffing to split the sector. Supervisors did not do enough to slow the sector down; TMU did not do enough to slow the sector down. This is one of the worst situations I have been put in in my XX years as a controller. People should be held responsible for the out of control sector. This event should not have happened. This event was damaging to my health. I think something like this should never be allowed to happened again; and there should be an investigation into how so many airplanes can be allowed in a sector that was already overloaded with traffic. I often asked for a couple minutes to stop the traffic and let me catch up. I several times asked for help from the D side and the Tracker neither one seemed to have any idea what was happening. There should be national flow initiatives to slow the traffic down to these saturated airports. Planes should have to wait safely on the ground. This can not be that hard to figure out. They can safely flow planes to all the ZZZ4 airports; they sure as hell can figure out how to do it to South ZZZ5 airports. Staffing needs to be returned to normal ASAP. TMU needs to get their act together. If the chief of the facility gets this; he does not need to look any further then this session to see that TMU is broken in this building. I was flying Aircraft X; at this time. During our arrival into ZZZ6 we were on the ZZZZZ STAR talking to ZZZ Center. The controller was very busy and I would say over loaded. He instructed us to descend to 10;000 ft. so we did as we were approaching the inner 10 mile ring on the TFR we radioed many times asking for lower and waiting to be handed off to ZZZ7 Approach. When he finally handed us off we apparently entered the 10 mile ring just as ZZZ7 approach replied to us. We were instructed to turn right I believe to a 250 heading and descend to 8;000 ft. As I started the turn I got a RA and was told I was being followed by the Aircraft Y. I was then asked to descend to 5;000 ft. and he radioed the fighter that he now had radio contact with me and was released. He continued to vector us to land at ZZZ6 and told me to call Phone Number. When I parked the aircraft I called and told him what had happened. I then had a interview with the government agency and told them what had happened. We were in and out of the clouds on the arrival and with as busy as the controller was he never gave us the hand off until it was to late. Knowing we were close to the TFR and the airspace and controller was saturated we could not make any abrupt turns to avoid the situation and could not get the controller to answer us in time to get properly vectored around. Captain reported due to ATC workload and failed communications; Captain entered TFR.